# a glider with a mass of 5 kg is moving to the right on a horizontal frictionless surface at 6 m/s when it collides with a 8 kg glider that is at rest. After the collision, the 8kg glider is moving to the right at 6 m/s. what are the speed and direction of the 5 kg glider ?

## before collision the light glider has kinetic energy of

(1/2)5(36)

there is no way the final kinetic energy of the system can be more than that

but you say
the heavy glider has speed 6 AFTER collision
(1/2)8(36)

That is impossible so there is no point in doing the conservation of momentum thing, which is also impossible.
You have a major typo I think.

## Given:

M1 = 5kg, V1 = 6 m/s.
M2 = 8kg, V2 = 0.
V3 = Velocity of M1 after the collision.
V4 = 6 m/s. = Velocity of M2(8kg) after the collision.

M1*V1 + M2*V2 = M1*V3 + M2*V4.
5*6 + 8*0 = 5*V3 + 8*6,
5*V3 = -18,
V3 = -3.6 m/s(Left) = Velocity of M1(5kg) after the collision.

## To determine the speed and direction of the 5 kg glider after the collision, we can apply the principle of conservation of linear momentum, which states that the total momentum before the collision is equal to the total momentum after the collision.

First, let's find the momentum before the collision. Momentum (p) is calculated by multiplying the mass (m) of an object by its velocity (v).

For the 5 kg glider:
Momentum (p1) = mass (m1) * velocity (v1) = 5 kg * 6 m/s = 30 kg*m/s (to the right)

For the 8 kg glider:
Momentum (p2) = mass (m2) * velocity (v2) = 8 kg * 0 m/s = 0 kg*m/s (initially at rest)

Now, let's find the total momentum before the collision:
Total initial momentum (p_initial) = p1 + p2 = 30 kg*m/s + 0 kg*m/s = 30 kg*m/s (to the right)

According to the conservation of momentum, the total momentum after the collision should be equal to the total initial momentum.

After the collision, the 8 kg glider is moving to the right at 6 m/s. Let's denote the speed and direction of the 5 kg glider as v_f and the direction as R (right).

Now, we can calculate the momentum after the collision. For the 8 kg glider, the momentum is:

p2_f = m2 * v2_f = 8 kg * 6 m/s = 48 kg*m/s (R)

For the 5 kg glider, the momentum is:

p1_f = m1 * v1_f = 5 kg * v_f

Since the gliders are moving in opposite directions (opposite momenta), the momentum for the 5 kg glider will be subtracted.

Total final momentum (p_final) = p1_f - p2_f = 5 kg * v_f - 48 kg*m/s

According to the conservation of momentum, the total final momentum should be equal to the total initial momentum:

p_final = p_initial
5 kg * v_f - 48 kg*m/s = 30 kg*m/s

Now, we solve for v_f:

5 kg * v_f = 30 kg*m/s + 48 kg*m/s
5 kg * v_f = 78 kg*m/s
v_f = 78 kg*m/s / 5 kg
v_f = 15.6 m/s (to the right)

Therefore, the speed of the 5 kg glider after the collision is 15.6 m/s to the right.